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Using Neuron Spiking Activity to Trigger Closed-Loop Stimuli in Neurophysiological Experiments

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Finite-Time Synchronization for Delayed Complex Dynamical Networks With Synchronizing or Desynchronizing Impulses.

Dan Yang, Xiaodi Li, Shiji Song

IEEE Transactions on Neural Networks and Learning Systems

|October 20, 2020

Summary

This summary is machine-generated.

This study addresses finite-time synchronization in complex dynamical networks with impulses. Synchronizing impulses accelerate synchronization, while desynchronizing impulses delay it, with controllers designed for both.

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Area of Science:

Complex Dynamical Networks (CDNs)
Control Theory
Network Synchronization

Background:

Investigates the finite-time synchronization of complex dynamical networks (CDNs) with impulses.
Addresses challenges posed by state discontinuities due to synchronizing and desynchronizing impulses.
Highlights the inapplicability of classical finite-time stability results in impulsive systems.

Purpose of the Study:

To establish sufficient conditions for achieving finite-time synchronization in CDNs with impulses.
To design memory controllers for managing both synchronizing and desynchronizing impulses.
To estimate the upper bounds of settling time for synchronization based on impulse sequences.

Main Methods:

Application of impulsive control theory and finite-time stability theory.
Design of two types of memory controllers tailored for synchronizing and desynchronizing impulses.
Analysis of impulse sequences to estimate synchronization settling times.

Main Results:

Sufficient conditions for finite-time synchronization in delayed CDNs with impulses are established.
Synchronizing impulses are shown to shorten the synchronization settling time.
Desynchronizing impulses are demonstrated to delay the synchronization settling time.

Conclusions:

The study provides a theoretical framework for finite-time synchronization in complex dynamical networks with impulses.
The developed controllers effectively manage impulsive effects on synchronization.
Simulation examples validate the theoretical findings on impulse-induced synchronization dynamics.